期刊文献+

一维半线性双曲型方程未知源的反问题

INVERSE PROBLEM OF DETERMINATION OF UNKNOWN SOURCE TERM FOR ONE-DIMENSIONAL HYPERBOLIC HALF-LINEAR EQUATION
原文传递
导出
摘要 We concern the inverse problem of determination of unknown source term for one-dimensional hyperbolic half-linear equation. Approach form for inverse problem is given by using correlative problem of assistant. We concern more ordinary problem than this paper, which is turned into integral equation with the method of characteristic line. We prove the existence and uniqueness of part solution for inverse problem, and unknown source can be solved bv successive approximation. We concern the inverse problem of determination of unknown source term for one-dimensional hyperbolic half-linear equation. Approach form for inverse problem is given by using correlative problem of assistant. We concern more ordinary problem than this paper, which is turned into integral equation with the method of characteristic line. We prove the existence and uniqueness of part solution for inverse problem, and unknown source can be solved by successive approximation.
出处 《计算数学》 CSCD 北大核心 2004年第3期329-336,共8页 Mathematica Numerica Sinica
基金 黑龙江省自然科学基金(No.F0215) 黑龙江省青年基金(No.QC03C03)资助项目。
关键词 偏微分方程 未知源 反问题 半线性双曲型方程 partial differential equation, unknown source, inverse problem
  • 相关文献

参考文献9

  • 1Y.M. Chen and G.Q. Xie, An iterative numerical algorithm for solving inverse problem of two-dimensional wave equation[J], J Comp Phys, 50:1(1983), 193-209.
  • 2Y.M. Chen, A versatile numerical method for solving inverse problem of partial differential equations[M], SIAM Philadelphia, 1984.
  • 3T. Suzuki, Inverse problem for heat equation on compact intervals and on circles[J], J Math Soc Japan, 1(1986), 39-65.
  • 4J.R. Cannon and P. Duchateau, An inverse problem for an unknown source term in a wave equation[J], J. Appl. Math., 43:3(1983), 553-564.
  • 5J. Fritz, Plane waves and spherical mean's applied to partial differential equation[M],Interscience publishers, Springer verlag, 1981.
  • 6F. Treves, Basic linear partial differential equations[M], Academic press, 1975.
  • 7H.M.Lieberstein.偏微分方程理论[M].高等教育出版社,1983..
  • 8吴建成,蔡日增,郑家茂.求解二维波动方程正演反演问题的半离散方法[J].应用数学,1998,11(2):66-70. 被引量:1
  • 9吴建成,蔡日增.求解高维波动方程的半离散方法[J].应用数学和力学,1998,19(5):457-464. 被引量:1

二级参考文献6

  • 1张关泉.波动方程的上行波和下行波的耦合方程组[J].应用数学学报,1993,16(2):251-263. 被引量:46
  • 2马在田,地震成像技术.有限差分法偏移,1989年
  • 3谢干权,中国科学.A,1988年,16卷,12期,1253页
  • 4郭本瑜,偏微分方程的差分方法,1988年,1,300页
  • 5吴建成,张大力,刘家琦.一维波动方程反问题求解的正则化方法[J]计算物理,1995(03).
  • 6谢干权,李建华.声波方程系数逆演问题的非线性积分方程及时卷特征迭代法(TCC)[J]中国科学(A辑 数学 物理学 天文学 技术科学),1988(12).

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部